The Axiom of Consent: Friction Dynamics in Multi-Agent Coordination

TL;DR

The paper develops a unified, dynamical theory of coordination under heterogeneous preferences through a single axiom: actions affecting agents require consent weighted by stake. It introduces the kernel triple $(\alpha, \sigma, \varepsilon)$ (alignment, stake, entropy) and derives the friction function $F = \sigma \cdot \frac{1+\varepsilon}{1+\alpha}$, linking consent structure to coordination difficulty. The Replicator-Optimization Mechanism (ROM) describes evolutionary dynamics over coordination configurations, predicting convergence to consent-respecting equilibria and highlighting cross-scale lumpability and belief-transfer effects. Domain-instantiations in multi-agent coordination, cryptocurrency governance, and political systems illustrate the framework’s generality, and the measurement apparatus offers operationalization of alignment, stakes, entropy, and friction for falsifiable empirical tests. The work provides a cross-domain, dynamical, and testable theory of coordination under preference heterogeneity with implications for AI alignment, distributed design, and governance.

Abstract

Multi-agent systems face a fundamental coordination problem: agents must coordinate despite heterogeneous preferences, asymmetric stakes, and imperfect information. When coordination fails, friction emerges: measurable resistance manifesting as deadlock, thrashing, communication overhead, or outright conflict. This paper derives a formal framework for analyzing coordination friction from a single axiom: actions affecting agents require authorization from those agents in proportion to stakes. From this axiom of consent, we establish the kernel triple $(α, σ, ε)$ (alignment, stake, and entropy) characterizing any resource allocation configuration. The friction equation $F = σ (1 + ε)/(1 + α)$ predicts coordination difficulty as a function of preference alignment $α$, stake magnitude $σ$, and communication entropy $ε$. The Replicator-Optimization Mechanism (ROM) governs evolutionary selection over coordination strategies: configurations generating less friction persist longer, establishing consent-respecting arrangements as dynamical attractors rather than normative ideals. We develop formal definitions for resource consent, coordination legitimacy, and friction-aware allocation in multi-agent systems. The framework yields testable predictions: MARL systems with higher reward alignment exhibit faster convergence; distributed allocations accounting for stake asymmetry generate lower coordination failure; AI systems with interpretability deficits produce friction proportional to the human-AI alignment gap. Applications to cryptocurrency governance and political systems demonstrate that the same equations govern friction dynamics across domains, providing a complexity science perspective on coordination under preference heterogeneity.

Figures (1)

• Figure 1: Reward gap across alignment ($\alpha$) and stakes ($\sigma$) conditions. Higher values indicate greater coordination failure. The pattern confirms theoretical predictions: friction increases with stakes (left to right) and decreases with alignment (top to bottom). Preliminary results from reduced sweep; full factorial results available at repository.

Theorems & Definitions (110)

• Definition 2.2: Alignment
• Definition 2.3: Aggregate Alignment
• Definition 2.4: Friction
• Proposition 2.1: Zero Friction Condition
• proof
• Proposition 2.2: Alignment Effect
• proof
• Proposition 2.3: Stake Effect
• proof
• Proposition 2.4: Entropy Effect